ebnm_npmle: Solve the EBNM problem using the family of all distributions

Description

Solves the empirical Bayes normal means (EBNM) problem using the family of all distributions. Identical to function ebnm with argument prior_family = "npmle". For details about the model, see ebnm.

Usage

ebnm_npmle(
  x,
  s = 1,
  scale = "estimate",
  g_init = NULL,
  fix_g = FALSE,
  output = ebnm_output_default(),
  optmethod = NULL,
  control = NULL
)

Value

An ebnm object. Depending on the argument to output, the object is a list containing elements:

data: A data frame containing the observations x and standard errors s.
posterior: A data frame of summary results (posterior means, standard deviations, second moments, and local false sign rates).
fitted_g: The fitted prior $\hat{g}$.
log_likelihood: The optimal log likelihood attained, $L(\hat{g})$.
posterior_sampler: A function that can be used to produce samples from the posterior. The sampler takes a single parameter nsamp, the number of posterior samples to return per observation.

S3 methods coef, confint, fitted, logLik,

nobs, plot, predict, print, quantile,

residuals, simulate, summary, and vcov

have been implemented for ebnm objects. For details, see the respective help pages, linked below under See Also.

Arguments

x: A vector of observations. Missing observations (NAs) are not allowed.
s: A vector of standard errors (or a scalar if all are equal). Standard errors may not be exactly zero, and missing standard errors are not allowed.
scale: The nonparametric family of all distributions is approximated via a finite mixture of point masses $$\pi_1 \delta_{\mu_1} + \ldots + \pi_K \delta_{\mu_K},$$ where parameters $\pi_k$ are estimated and the point masses are evenly spaced over $(\mu_1, \mu_K)$. By taking a sufficiently dense grid of point masses, one can obtain an arbitrarily good approximation. The distance between successive point masses can be specified by the user via parameter scale, in which case the argument should be a scalar specifying the distance $d = \mu_2 - \mu_1 = \cdots = \mu_K - \mu_{K - 1}$; alternatively, if scale = "estimate", then ebnm sets the grid via function ebnm_scale_npmle.
g_init: The prior distribution $g$. Usually this is left unspecified (NULL) and estimated from the data. However, it can be used in conjuction with fix_g = TRUE to fix the prior (useful, for example, to do computations with the "true" $g$ in simulations). If g_init is specified but fix_g = FALSE, g_init specifies the initial value of $g$ used during optimization. This has the side effect of fixing the scale parameter. When supplied, g_init should be an object of class normalmix or an ebnm object in which the fitted prior is an object of class normalmix.
fix_g: If TRUE, fix the prior $g$ at g_init instead of estimating it.
output: A character vector indicating which values are to be returned. Function ebnm_output_default() provides the default return values, while ebnm_output_all() lists all possible return values. See Value below.
optmethod: Not used by ebnm_npmle.
control: A list of control parameters to be passed to optimization function mixsqp.